Question

An arc subtends a central angle measuring 2pi/3

radians.
What fraction of the circumference is this arc?
of the circumference

Answer 1

1/3

Explanation:

We know that angle subtended by whole circumference is
`2\pi`.

If r is the radius then Length of whole circumference is
`2\pi r`

`2\pi` radian has
`2\pi r` length

dividing both side by
`2\pi` we have

`2\pi /2\pi = 2\pi r/2\pi \ circumference`

1 radian has r length

1 radian = r length equation a

=> since we have to find value of circumference for
`2\pi /3` we

multiply both side of equation a with
`2\pi /3`.

`2\pi /3 \radian = r* 2\pi /3 \circumference`

therefore, length of required arc is
`2\pi r/3`

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we have to find how much is this as fraction of total circumference of circle

fraction of circumference = value of arc length / total length of circumference

fraction of circumference =
`=>(2\pi r/3) / 2\pi r\\=> 1/3`

Thus, the given arc is 1/3 of circumference of circle.